Add to Array-Form of Integer

Add to Array-Form of Integer

What is this problem about?

In the Add to Array-Form of Integer coding problem, an integer is represented as an array of its digits (e.g., $123$ is [1, 2, 3]). You are also given a standard integer $K$. You need to add $K$ to the array-form number and return the result in the same array-form.

Why is this asked in interviews?

This question is popular at Google and Bloomberg because it tests array manipulation and basic math synchronization. It evaluates whether you can gracefully merge two different data structures—an array and a primitive integer—without inefficiently converting between them.

Algorithmic pattern used

The Array and Math interview pattern is the primary approach. You iterate through the array from the last index to the first, adding $K$ to the current digit. The new digit is the result modulo 10, and the new "carry" (or updated $K$) is the result divided by 10.

Example explanation

Suppose num = [2, 1, 5] and K = 806.

1. Start at the end of num: $5 + 806 = 811$. New digit is $1$, carry $81$.
2. Next digit: $1 + 81 = 82$. New digit is $2$, carry $8$.
3. Next digit: $2 + 8 = 10$. New digit is $0$, carry $1$.
4. Since we have a leftover carry of $1$, we prepend it to the array. Final Result: [1, 0, 2, 1].

Common mistakes candidates make

• Integer Overflow: Converting the array into a single integer, adding $K$, and then converting back. If the array has 10,000 digits, this is impossible.
• Stopping too early: If the array is exhausted but $K$ still has remaining digits (the carry), many candidates forget to continue appending those digits to the front of the result.

Interview preparation tip

Think of $K$ itself as the "carry." Instead of maintaining a separate boolean or single-digit carry variable, just keep adding $K$ to the digits and updating $K = K / 10$ at each step.